Algebraic and PDE approaches for lattice scale-spaces with global constraints

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dc.contributor.author Maragos, P en
dc.date.accessioned 2014-03-01T01:18:37Z
dc.date.available 2014-03-01T01:18:37Z
dc.date.issued 2003 en
dc.identifier.issn 0920-5691 en
dc.identifier.uri http://hdl.handle.net/123456789/15109
dc.subject Lattice operators en
dc.subject Levelings en
dc.subject Morphology en
dc.subject Nonlinear scale-spaces en
dc.subject PDEs en
dc.subject.classification Computer Science, Artificial Intelligence en
dc.subject.other Algorithms en
dc.subject.other Computer vision en
dc.subject.other Constraint theory en
dc.subject.other Convergence of numerical methods en
dc.subject.other Feature extraction en
dc.subject.other Image analysis en
dc.subject.other Image enhancement en
dc.subject.other Image segmentation en
dc.subject.other Linear algebra en
dc.subject.other Mathematical operators en
dc.subject.other Object recognition en
dc.subject.other Partial differential equations en
dc.subject.other Image simplification en
dc.subject.other Lattice operators en
dc.subject.other Motion analysis en
dc.subject.other Nonlinear scale spaces en
dc.subject.other Object detection en
dc.subject.other Shape analysis en
dc.subject.other Mathematical morphology en
dc.title Algebraic and PDE approaches for lattice scale-spaces with global constraints en
heal.type journalArticle en
heal.identifier.primary 10.1023/A:1022999923439 en
heal.identifier.secondary http://dx.doi.org/10.1023/A:1022999923439 en
heal.language English en
heal.publicationDate 2003 en
heal.abstract This paper begins with analyzing the theoretical connections between levelings on lattices and scale-space erosions on reference semilattices. They both represent large classes of self-dual morphological operators that exhibit both local computation and global constraints. Such operators are useful in numerous image analysis and vision tasks including edge-preserving multiscale smoothing, image simplification, feature and object detection, segmentation, shape and motion analysis. Previous definitions and constructions of levelings were either discrete or continuous using a PDE. We bridge this gap by introducing generalized levelings based on triphase operators that switch among three phases, one of which is a global constraint. The triphase operators include as special cases useful classes of semilattice erosions. Algebraically, levelings are created as limits of iterated or multiscale triphase operators. The subclass of multiscale geodesic triphase operators obeys a semigroup, which we exploit to find PDEs that can generate geodesic levelings and continuous-scale semilattice erosions. We discuss theoretical aspects of these PDEs, propose discrete algorithms for their numerical solution which converge as iterations of triphase operators, and provide insights via image experiments. en
heal.publisher KLUWER ACADEMIC PUBL en
heal.journalName International Journal of Computer Vision en
dc.identifier.doi 10.1023/A:1022999923439 en
dc.identifier.isi ISI:000181764500004 en
dc.identifier.volume 52 en
dc.identifier.issue 2-3 en
dc.identifier.spage 121 en
dc.identifier.epage 137 en

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